Related papers: Duality in mass-action networks
We discuss the notion of duality and selfduality in the context of the dual projection operation that creates an internal space of potentials. Contrary to the prevailing algebraic or group theoretical methods, this technique is applicable…
As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into…
We consider a class of multi-type particle systems having similar structure to the contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We give two additional…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
Cascades are self-amplifying processes triggered by feedback mechanisms that may cause a substantial part of a macroscopic system to change its phase in response of a relatively small local event. The theoretical background for these…
In this report we study the dual equivalence between the generalized self-dual (SD) and topologically massive (TM) models. To this end we linearize the model using an auxiliary field and apply a gauge embedding procedure to construct a…
Using examples of a D=2 chiral scalar and a duality-symmetric formulation of D=4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D=4 case, upon performing a duality transform of an…
Real world complex networks often exhibit multiplex structure, connecting entities from different aspects of physical systems such as social, transportation and biological networks. Little is known about general properties of such networks…
We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine-structure constant is rational, the theory admits non-invertible symmetries which can be realized as composites of…
A mesh motion model based on deep operator networks is presented. The model is trained on and evaluated against a biharmonic mesh motion model on a fluid-structure interaction benchmark problem and further evaluated in a setting where…
We construct projective limit of projective sequence in the following categories: Archimedean order unit spaces with unital positive maps and operator systems with unital completely positive maps. We prove that inductive limit and…
There exists a well-known duality between the Maxwell-Chern-Simons theory and the self-dual massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This…
A net in $\mathbb{P}^2$ is a configuration of lines $\mathcal A$ and points $X$ satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac-Moody…
Four-dimensional N=2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in…
For a finite abelian group action on a linear category, we study the dual action given by the character group acting on the category of equivariant objects. We prove that the groups of equivariant autoequivalences on these two categories…
We revisit the total scatterings (in terms of extinction, scattering and absorption cross sections) by arbitrary clusters of nonmagnetic particles that support optically-induced magnetic responses. Our reexamination is conducted from the…
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…
Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here for homogeneous networks, by showing that every homogeneous…
We introduce a structure termed ``connected cyclic diagonal'' on a chain complex, which induces stable power operations in its cohomology with the property that negative power operations consistently vanish. This chain level structure is…
We develop a general duality between neural networks and compositional kernels, striving towards a better understanding of deep learning. We show that initial representations generated by common random initializations are sufficiently rich…